This data set displays the violent crime rates per 100,000 residents by US State in 1973.

There are 4 variables with 50 states in this data set:

• murder
  
• assault
  
• rape
  
• urban population

Is there a correlation between the violent crime rates and each other?

• rape vs murder
  
• murder vs assault
  
• assault vs rape
  

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.800   4.075   7.250   7.788  11.250  17.400

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    45.0   109.0   159.0   170.8   249.0   337.0

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    7.30   15.07   20.10   21.23   26.18   46.00

boxplot(USArrests$Murder, horizontal = TRUE, xlab = "Rate 
        (cases/100,000 people)", main = "Murder Crimes", col = "red") 
summary(USArrests$Murder) 

boxplot(USArrests$Assault, horizontal = TRUE, xlab = "Rate 
        (cases/100,000 people)", main = "Assault Crimes", col = 
          "orange") 
summary(USArrests$Assault) 

boxplot(USArrests$Rape, horizontal = TRUE, xlab = "Rate 
        (cases/100,000 people)", main = "Rape Crimes", col = "gold") 
summary(USArrests$Rape) 

I decided to do 3 separate boxplots and summaries to make the data easier to read and understand it instead of putting it all together. I excluded the urban population data because it was not a variable I was discussing.

This scatter plot displays a positive correlation between the rate of rape and murder crimes.

This scatter plot displays a positive correlation between the rate of assault and murder crimes.

This scatter plot displays a positive correlation between the rate of assault and rape crimes.

murderRates <- USArrests$Murder
rapeRates <- USArrests$Rape

x = rapeRates
y = murderRates

plot_ly(x = x, y = y, type = "scatter", mode = "markers") %>%
  add_trace(x = rapeRates, y = predict(lm(murderRates~rapeRates)), 
            mode = "lines", type = "scatter", line = list(color = 
            "Red")) %>%
        layout(title = "Correlation between Murder and Rape Crimes in 
        the US", xaxis = list(title = "Rape Rates"), yaxis = list
          (title = "Murder Rates"))

assultRates <- USArrests$Assault
murderRates <- USArrests$Murder

x = assultRates
y = murderRates

plot_ly(x = x, y = y, type = "scatter", mode = "markers") %>%
  add_trace(x = assultRates, y = predict(lm(murderRates~assultRates)), 
            mode = "lines", type = "scatter", line = list(color = 
            "Red")) %>%
        layout(title = "Correlation between Assault and Murder Crimes 
        in the US", xaxis = list(title = "Assault Rates"), yaxis = 
          list(title = "Murder Rates"))

assultRates <- USArrests$Assault
rapeRates <- USArrests$Rape

x = assultRates
y = rapeRates

plot_ly(x = x, y = y, type = "scatter", mode = "markers") %>%
  add_trace(x = assultRates, y = predict(lm(rapeRates~assultRates)), 
            mode = "lines", type = "scatter", line = list(color = 
            "Red")) %>%
        layout(title = "Correlation between Assault and Rape Crimes 
        in the US", xaxis = list(title = "Assault Rates"), yaxis = 
          list(title = "Rape Rates"))

I decided that scatterplots would be the best way to analyze whether there was a correlation with a linear regression model included.

Rape vs Murder

## R-squared value: 0.3176211

Assault vs Murder

## R-squared value: 0.6430008

Assault vs Rape

## R-squared value: 0.4425459

assultRates <- USArrests$Assault
rapeRates <- USArrests$Rape
murderRates <- USArrests$Murder

x1 = assultRates
y1 = rapeRates
y2 = murderRates

lm_model <- lm(y2~y1, data = USArrests)
r_squared <- summary(lm_model)$r.squared
cat("R-squared value:", r_squared, "\n")

Assuming:

• The size of error doesn’t change significantly across the values.
  
• There are no hidden relationships among the variables.
  
• The data has a normal distribution.
  
• The Relationship between the variables are linear.
  
  

There seems to be a positive correlation between all crimes in this data set, which answers my question of whether each violent crime has some type of correlation with one another.